Flow Structures Extracted from Visualization Images: Vector Fields and Topology

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1 Flow Structures Extracted from Visualization Images: Vector Fields and Topology Tianshu Liu Department of Mechanical & Aerospace Engineering Western Michigan University, Kalamazoo, MI 49008, USA

2 We live in the fascinating world of fluids. Air Water

3 Interaction between Fluid Flow and Surface in Engineering Systems (e.g. Aircraft) Velocity vector field Skin-friction vector field Surface pressure field

4 Motions of fluids are complex and intriguing. Phenomenologically, there are multiplescale, highly deforming interacting structures, such as turbulence (one of the most challenging problems in physical sciences). The Navier-Stokes equations remain one of the most difficult problems in mathematics. Flows in air and water cannot be observed directly.

5 Flow Visualizations make flows optically observable by using tracers. Particles, smoke, dyes, bubbles etc. Luminescent molecules Fluid density change Oil, sublimating coatings, oxygen- and temperature-sensitive coatings

6 Natural Flow Visualizations

7 Laboratory Flow Visualizations in Space

8 Laboratory Flow Visualizations on Surface Luminescent-oil visualizations Surface sublimation & dye visualizations

9 Global Measurements of Vector Fields and Derived Quantities in Fluid Mechanics & Aerodynamics Velocity field Skin friction field Magic Vision System Surface pressure field Surface temperature/ heat flux field JAL

10 Technical Objective To develop a unified theoretical framework for high-resolution flow diagnostics based on various flow visualizations Methodology Mathematical models for flow visualizations Inverse problem for extraction of vector fields (velocity & skin friction fields) Global velocity diagnostics Global skin friction diagnostics

11 Mathematical Modeling of Imaging Process in Flow Visualizations: Projection Method from Object Space to Image Geometrical or Perspective Radiometric

12 Transport Equations for Flows Projection Projected Motion Equations Physics-Based Optical Flow Equation in Image Plane g f ( x,x,g ) g / t u 1 2 Optical flow Optical flow has a clear physical meaning: Velocity or Skin-friction Normalized image intensity

13 The Inverse Problem to Solve the Generic Physics-Based Optical Flow Equation g f ( x,x,g ) g / t u 1 2 Variational Method Functional for minimization: J( u ) g / t g u f 2 dx 1 dx 2 u1 u2 dx1dx2 2 Smooth Constraint 2

14 Euler-Lagrange Equation g 2 g / t ( gu ) f 0 u Neumann boundary condition: u/n 0 Numerical solution: Finite difference & Jacob iteration

15 Global Velocity Diagnostics Examples Flow Structures of Jupiter s Great Red Spot Global Velocity Measurements in Full-Scale Automotive Wind Tunnel

16 Jupiter s Atmosphere Images Taken by NASA s Voyager Spacecraft Great Red Spot (GRS) White Ovals

17 NASA Galileo 1996 Images of the GRS t = 0 s t = 4320 s

18 The GRS s Unique Flow Structure: Hollow Vortex High-speed, near-elliptical, anti-cyclonical collar Low-speed inner region Velocity Vectors (resolution reduced by 4)

19 The Intriguing Counter-Rotational Motion Near the Center of the GRS (observed in 40 years) Dynamical role of cyclonic, counter-rotational motion near the center??

20 Cyclonic Motion & Outward Spiraling Source Node Counter-Rotating Motion Cyclonic Source Node

21 Topology of Vector Field om Surface: The Poincare-Bendixson Index Formula A conservation law between the number of the singular points in a region and the number of the switch points on the boundary: Topological Constraint: # N # S 1 Consequence: One long-lived node necessary for the existence of the GRS

22 Cyclonic Source Node & Convention Instability In a Lagrangian sense by following a fluid parcel along z to a source node, w / z where N 2 t 0 ( N 2 g / [ z(t' T ) )]dt' T / z g / (N is the buoyancy frequency) The surface vorticity at a source node: s f 2 o N 2 s ( w / z ) 0 0 c p Cyclonic Rotation Convection Instability The relative vorticity is intensified by the convection-induced stretching of the planetary vorticity associated with the Coriolis force.

23 Saturn s North Polar Vortex & Hexagon Hexagon North Polar Vortex

24 Velocity Field of Saturn s North Polar Vortex

25 Extracting High-Resolution Velocity Fields on a Full-Scale Car Based on Smoke Visualization Optical Flow Diagnostics: Large regions at one vector per pixel) PIV Diagnostics Small diagnostic regions: Problem in full-scale wind tunnels

26 Flow over Car in Full-Scale Wind Tunnel Image 1 Image 2 Velocity Vectors Extracted by Using Optical Flow Method

27 Summary on Global Velocity Diagnostics Using Optical Flow Method General method for extracting velocity fields based the physics-based optical flow equation Application to various flow visualization images High resolution (one vector at each pixel) Tomographic reconstruction of 3D velocity fields

28 Skin Friction Fields in Nature and Engineering Systems Source of drag of aircraft Formation of topographic patterns

29 Extraction of Skin Friction Fields from Surface Flow Visualizations A More Challenging Problem Global luminescent oil-film (GLOF) visualization Surface heat transfer visualization with temperature sensitive paint (TSP) Surface mass transfer visualization with pressure sensitive paint (PSP) Surface mass transfer visualization with sublimation coatings Surface pressure visualization with PSP

30 Skin Friction Diagnostics Examples Junctions Flows Delta Wings

31 Square Cylinder Junction Flow Experimental Setup Typical Luminescent Oil Image Local Re: Re = Square Size: 51 by 51 mm

32 Square Cylinder Junction Flow Skin Friction Vectors Skin Friction Magnitude (fusion of 300 snapshot solutions)

33 Square Cylinder Junction Flow Skin Friction Lines

34 Wing-Body Junctions in Engineering Systems Junctions

35 Luminescent Oil Visualization in Wing-Body Junction Flow Luminescent Oil Intensity Distribution Surface Mesh (240,372 grid points)

36 Multiple-View-Reconstructed Skin Friction Field on the Wing-Body Junction Model for AoA = 6 deg # N # S 6 6 # N # S 0

37 Zoomed-in Views of Topological Details (AoA = 6 deg) Region A Region B # N # S 1 ( # Z # Z ) / 2 1 # N # S 1 ( # Z # Z ) / 2 0

38 Zoomed-in Views of Topological Details (AoA = 6 deg) Region C Region D # N # S 1 ( # Z # Z ) / 2 1 # N # S 1 ( # Z # Z ) / 2 0

39 Delta Wings in High-Speed Aircraft Enhanced Vortex Lift Leading-edge vortices

40 65 o Delta Wing Typical Luminescent Oil Image Skin Friction Lines Secondary separation line Reattachment line AoA = 13 deg (Re c = 300,000) AoA = 13 deg

41 65 o Delta Wing Vortex Bursting AoA = 15 deg AoA = 20 deg

42 Skin Friction & Surface Pressure Gradient Surface pressure gradient and skin friction are intrinsically coupled mainly through a vorticity- Dynamic quantity namely the boundary enstrophy flux (BEF). Optical Flow Equation in the Image Plane G ˆ j p / x j 0 where G f BEF

43 PSP Pressure Field Pressure Gradient Field

44 Skin Friction Field on a 70-deg Delta Wing at Mach 0.55 for AoA = 20 deg

45 Summary on Global Skin Friction Diagnostics Global luminescent oil-film (GLOF) method has been used for skin friction diagnostics in complex separated flows The mass- and heat-transfer methods is also promising for global skin friction diagnostics These methods could be extended to supersonic and hypersonic flows and water flows

46 Conclusions :Toward a Unified Approach: Physics-Based Optical Flow Method Various Flow Visualization Techniques Velocity field Skin friction field Surface pressure field Surface temperature/heat flux field

47 Skin Friction & Natural Surface Patterns??? Thank You! More Questions?